Abstract

It is shown that substructural logics of $k$-potent BL-algebras and $k$-potent hoops have unitary unification while Basic Fuzzy Logic, BL, and $\infty$-valued {\L}ukasiewicz logic do not have unitary unification. It follows that every $k$-potent substructural logic containing BL is structurally complete in the restricted sense, but Basic Logic itself is not.